Delve into the second lecture of the Modern Numerical Methods in Computational Relativity series, delivered by Geoffrey Lovelace as part of the Summer School on Gravitational-Wave Astronomy. Explore advanced techniques and methodologies used in solving complex equations of General Relativity and magnetohydrodynamics through supercomputer simulations. Gain insights into the crucial role of Numerical Relativity in modeling high-energy astrophysical phenomena such as black hole mergers, neutron star collisions, and massive star collapses. Understand the significance of these simulations in interpreting gravitational-wave signals and multi-messenger observations. Benefit from this graduate-level course, designed for students and researchers in gravitational-wave astrophysics, offering a deep dive into the cutting-edge numerical methods shaping our understanding of the universe's most extreme events.